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3x-1/2x+4=7
We move all terms to the left:
3x-1/2x+4-(7)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
3x-1/2x-3=0
We multiply all the terms by the denominator
3x*2x-3*2x-1=0
Wy multiply elements
6x^2-6x-1=0
a = 6; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·6·(-1)
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{15}}{2*6}=\frac{6-2\sqrt{15}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{15}}{2*6}=\frac{6+2\sqrt{15}}{12} $
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